Nonlinear Models—Modifications of Delay Logistic Equations

Logistic equations have numerous applications, especially in population dynamics. In Chap. 11, several modifications of delay logistic equations are considered, in particular, both additive and multiplicative generalizations. In the study of the nonoscillation properties of nonlinear equations usually one of the following three methods is applied: first, a differential equation can be transformed into an operator equation with the following property: if the operator equation has a nonnegative solution, then the differential equation has a nonoscillatory solution, second, for the relevant operator equation either the Schauder Fixed-Point Theorem is applied, or convergence of monotone approximations to a solution is demonstrated, and, third, the connection of oscillation properties of nonlinear and linear delay differential equations can be employed. In this chapter, all the three methods are used. In the most difficult superlinear case the differential equation is transformed into an operator equation which incorporates both an increasing and a decreasing operators.